The Taylor transformation hybrid method applied for solving the Stefan problem

• Autorzy: Grzymkowski, R. , Hetmaniok, E. , Pleszczyński, M.
• Języki publikacji: EN

Abstrakty

EN

The paper presents the analytic-numerical hybrid method using, among others, the Taylor transformation, thanks to which the solution of the Stefan problem is replaced by the solution of a nonlinear system of equations.

Słowa kluczowe

PL

przekształcenie Taylora; przewodzenie ciepła; zagadnienie Stefana

EN

Taylor transformation; heat conduction; Stefan problem

• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2016
• Tom: Vol. 6, iss. 1
• Strony: 111--123
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Grzymkowski, R.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

autor

Hetmaniok, E.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

autor

Pleszczyński, M.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland,

Bibliografia

• 1. Grzymkowski R.: Taylor transformation and its applications. Jacek Skalmierski Computer Studio, Gliwice 2015 (in Polish).
• 2. Grzymkowski R., Hetmaniok E., Pleszczyński M.: Analytic-numerical method of determining the freezing front location. Arch. Foundry Eng. 11, no. 3 (2011), 75–80.
• 3. Grzymkowski R., Hetmaniok E., Pleszczyński M., Słota D.: A certain analytical method used for solving the Stefan problem. Therm. Sci. 17 (2013), 635–642.
• 4. Grzymkowski R., Pleszczyński M., Hetmaniok E.: Problem of the moving boundary in continuous casting solved by the analytic-numerical method. Arch. Foundry Eng. 13, no. 1 (2013), 33–38.
• 5. Grzymkowski R., Pleszczyński M., Słota D.: Application of the Adomian decomposition method for solving the heat equation in the cast-mould heterogeneous domain. Arch. Foundry Eng. 9, no. 4 (2009), 57–62.
• 6. Grzymkowski R., Pleszczyński M., Słota D.: The two-phase Stefan problem solved by the Adomian decomposition method. Proceedingsof the 15th IASTED International Conference Applied Simulation and Modelling, ACTA Press, Rhodos, 2006, 511–516.
• 7. Hetmaniok E., Słota D., Wituła R., Zielonka A.: Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem. Comput. Math. Appl. 61 (2011), 1931–1934.
• 8. Hetmaniok E., Słota D., Zielonka A., Wituła R.: Comparison of ABC and ACO Algorithms Applied for Solving the Inverse Heat Conduction Problem. Lect. Notes Comput. Sc. 7269 (2012), 249–257.
• 9. Majchrzak E., Mochnacki B., Dziewoński M., Jasiński M.: Identification of boundary heat flux on the continuous casting surface. Arch. Foundry Eng. 8, no. 4 (2008), 105–110.
• 10. Mendakiewicz J., Piasecka Belkhayat A., Szopa, R.: Modeling of the Stefan Problem Using the BEM. Solidification of Metals and Alloys 2, no. 44 (2000), 223–228.
• 11. Mochnacki B., Pawlak E.: Identification of boundary condition on the contact surface of continuous casting mould. Arch. Foundry Eng. 7 no. 4 (2007), 202– 206.
• 12. Słota D.: Solving the inverse Stefan design problem using genetic algorithms. Inverse Probl. Sci. En. 16 (2008), 829–846.